# networkx.algorithms.mis.maximal_independent_set¶

maximal_independent_set(G, nodes=None, seed=None)[source]

Returns a random maximal independent set guaranteed to contain a given set of nodes.

An independent set is a set of nodes such that the subgraph of G induced by these nodes contains no edges. A maximal independent set is an independent set such that it is not possible to add a new node and still get an independent set.

Parameters
• G (NetworkX graph)

• nodes (list or iterable) – Nodes that must be part of the independent set. This set of nodes must be independent.

• seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness.

Returns

indep_nodes – List of nodes that are part of a maximal independent set.

Return type

list

Raises
• NetworkXUnfeasible – If the nodes in the provided list are not part of the graph or do not form an independent set, an exception is raised.

• NetworkXNotImplemented – If G is directed.

Examples

>>> G = nx.path_graph(5)
>>> nx.maximal_independent_set(G)
[4, 0, 2]
>>> nx.maximal_independent_set(G, [1])
[1, 3]


Notes

This algorithm does not solve the maximum independent set problem.